Stock-to-flow model for BTC & LTC. Is LTC silver in crypto?

By October 22, 2021DeFi
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A lot of people cast a skeptical eye for S2F(stock-to-flow) model recently when the predected price of bitcoin started going off course the curve. S2F(stock-to-flow) ratio has been used for commodities and natural resources in traditional finance. Bitcoin has the finite supply. This means we’ve got the limited number of BTC supply and the amout of mining in every block can be also static until the next halving. It’s getting scarce & scarce and the system defined minable amounts in the underlying blockchain protocol from day one. Here was the starting point in PlanB’s article why we thought S2F could be applicable to BTC like other scarce assets in the market. [1]

Pantera Capital, a hedge fund that specializes in cryptocurrencies, predicted in April 2020 that bitcoin could rise to $115,000 by August this year, by using this model. Off course as you already know, BTC price came back around $60,000 but the price hasn’t skyrocketed to $115,000 level. Why? First of all, S2F model focuses on supply side asset scarcity and regression technique was applied to predict the future price. If there is no demand and buying power, supply means nothing. “Why do you want to buy a bottle of water if you’re not thirsty?” Also regression technique is a method to predict values from past data by learning the relationship between features, observations in data.

I’d like to test this S2F model for Litecoin(LTC) if S2F can be leveraged in general for crypto currency market. Using more profound approach will be a subject to future research.

Image by Jan from Pixabay.


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I wonder why people applied S2F for only Bitcoin. Off course people might say Bitcoin can only play a significant role in crypto currencies in the long run so other crypto currencies can’t be treated in the same manner. But some of other crypto currencies also have the finite supply and halving mechanism or depleting scheme in nature. This sounds to me, those assets also can be deemed as natural resources and they might be applicable to S2F model. I pick LTC(Litecoin) to apply S2F and confirm the differences by using the same simple regression technique.

At first, I reproduced Bitcoin s2f model by using Anaconda3 and built-in scikit-learn library. Please note that I calculated flow and S2F ratio in the obtained data points from CoinMetric API. So those culculated values might not be the same as other people have used including PlanB’s in the article. Also flow data was calculated by subtracting supply from previous months and multiply x12 to annualize assumed yearly produce. This is not a rigor calculation with block-based approach (for example, to estimate block production rate from the average block produce in Bitcoin).

Here are 2 x 2 scatter plots. The combination consists of actual numbers versus natural logarithm numbers and S2F against marketcap or S2F against price (Top left: s2f and marketcap in actual, Top right: s2f and price in actual, Bottom left: s2f and marketcap in log, Bottom right: s2f and price in log). I followed the same approach to do natural logarithm for values (not axes in this experiment) and found a clear linear relationship between ln(marketcap) or ln(price) and ln(s2f) as a result.

scatter plots for relationships between price, marketcap and s2f ratio

I used a simple regression technique and fit a model as below. As explained, data points must be different from the original article and I took data starting from 2010 August, which was available on the API. But the result is quite similar and does not look bad. The slope: 3.34754805 and the intercept: 14.138984154543218 were also fine (PlanB’s formula: ln(y) = 3.31954 ln(x) + 14.6227, R2 score was 0.947328). I’d like to take this as a baseline and extend it to Litecoin(LTC) in the next paragraph. If you want to predict the future price of Bitcoin, just call the model and give it future assumed S2F values. All codes are available in github to reproduce the result.

RMSE value: 0.9655475133041838
R2 score: 0.9290861664837493
Slope: [3.34754805], Intercept: 14.138984154543218
F-statistic: [1742.51558568], P-value: [2.68246322e-78]
linear regression fit for bitcoin price, marketcap and s2f ratio

Use stock-to-flow model for Litecoin(LTC)

First point was like… what if we use stock-to-flow model for Litecoin(LTC) but behind this I had the hypothesis that crypto currencies with the finite supply and mild inflation or depleting mechanism like natural resources will also face the same scarcity issue in the market. So stock-to-flow model can be applicable to some degree for not only Bitcoin but also other crypto currencies. I believe it’s worth to do the same test for other crypto like Cardano/ADA(45 billion ADA), Polygon/Matic(10 billion MATIC), or Vechain/VET(86,712,634,466 VET) that I’ll talk later.

Data points are different for Litecoin because old data points were not available on the API. I ran the same code to collect data starting from 2013 April. This may have impacted the result of the regression because some early days data were missing. I draw a line plot for each price, marketcap and S2F ratio as below. These are real numbers. Rather than S2F ratio value itself, I do see a chart pattern that the market cap and the price broke out and hit ATH sometime after the halving, and Litecoin’s S2F value is around 25 as of now.

line plot price, marketcap and s2f ratio

Here’s the quote from PlanB article and we confirm that the S2F value 25 is close to the silver’s S2F value 22. Silver’s market value is around 230 billion. In that article gold and silver dots could give some confidence for the linear relationship between ln(marketcap) and ln(s2f) for Bitcoin market. But from this scarce level (s2f=25), the price of Litecoin looks undervalued to me (off course this is only the angle from supply side as if natural resources).

What is very interesting is that gold and silver, which are totally different markets, are in line with the bitcoin model values for SF. This gives extra confidence in the model. Note that at the peak of the bull market in Dec 2017 bitcoin SF was 22 and bitcoin market value was $230bn, very close to silver.

Here are the same 2 x 2 scatter plots. The combination consists of actual numbers versus natural logarithm numbers and S2F against marketcap or S2F against price (Top left: s2f and marketcap in actual, Top right: s2f and price in actual, Bottom left: s2f and marketcap in log, Bottom right: s2f and price in log). I followed the same approach to do natural logarithm for values (not axes in this experiment) and found a clear linear relationship between ln(marketcap) or ln(price) and ln(s2f) as a result.

scatter plots for relationships between price, marketcap and s2f ratio

Mhh… there is no beauty in it. I don’t see any strong relation between ln(marketcap) and ln(s2f) for Litecoin even before fitting a model… let’s try modelling it now. R2 score is about 0.626 which is not good. The slope: 1.71572674 and the intercept: 16.934506876879198. When I looked at the right chart, I thought that the price followed the predicted price to some extent with the large deviations. It seems like the price movement is just lagging after the halving. The regression result was not precise but the S2F ratio can be still the dominant driving force factor for the price movement.

linear regression fit for bitcoin price, marketcap and s2f ratio

If we reckon with the adoption level and people’s perception about Litecoin, there might be room for Litecoin to catch up the expected marketcap around 240 billion, which is silver’s market size with S2F ratio 22. This ranks Litecoin the 3rd largest marketcap in the current list and a price per coin would be about 3,300 USD level. Off course there are a lot of factors not relying on only this regression model but also the dominance of tokens, demand in the market, regulations, etc. But if S2F model is legitimate to some degree for Bitcoin and similar assets, and when Litecoin is more widely known and adopted, this hypothesis would be realistic.

It’s explained in CoinMarketCap like “As of January 2021, Litecoin is one of the most widely accepted cryptocurrencies, and more than 2,000 merchants and stores now accept LTC across the globe”. It is getting useful and decent in the scene and I think it’s on the way to mass adoption. It is a matter of time.

Next. How about other cryptos? such as Cardano/ADA?

Are we seeing similarities between Bitcoin, Litecoin and ADA? Yes, these assets have the finite supply and inflation mechanism. While Bitcoin, Litecoin have the halving mechanism, ADA has its own inflation mechanism and the inflation rate will be decreasing time by time. Accoding to this article below, Cardano inflation rate is getting low and low, and it’s expected to be deflationary after 2030. We’ve got two formulas to calculate ADA inflation rate as following. [2]

  1. At any time, nor more than 0.3% of the reserve ADA will be released every Epoch (5 days), up to 0.3% of the reserve can be released in the Cardano network.
  2. The released ADA is equal til 0.3% muliplied by the percentage of the circulated supply of ADA being staked. The inflation rate will be converging to zero but never be zero.

Cardano is not deflationary, but it will be in 2030 and beyond. At the moment, the inflation rate is 5.7%. However, the inflation rate decreases exponentially over time and will be 0.9% per year in 2030. Assuming 1% of the supply is lost per year due to human error, Cardano will be deflationary.

Now you have noticed that ADA has a dynamic combination with the reserve and the proportion of stake in the circulating supply for the inflation mechanism. Here’s the table that I used to obtain data and applied the same function for ADA, the S2F value is not so stable like Bitcoin & Litecoin and it seems not to impact the price action (just 10 data points). But again, as same as Litecoin, I’d like to emphasize that S2F of ADA is a large number already. Let’s remember what S2F ratio means here. It means that with the current annual flow pace, it takes S2F years to catch up the current supply.

ADA has been scarce more than I thought in first place. The average S2F of these 10 data points is 41.241 so that 470 billion is the target market cap in theory. This means ADA has 10 USD per coin potential based on S2F model.

line plot price, marketcap and s2f ratio

Some guys may say, hey are you joking? there is no room in the crypto market for those other tokens to grow at that level. Because Bitcoin dominance has been around 50%(47.6% today) and will stay there as store of value. This is a significant role for Bitcoin to play in the longer term. I have heard that the total marketcap for crypto will be 10 trillion USD at maximum and not go beyond that. But to be conservetive, only bitcoin may conform to this policy as store of value from the fact that it has been compared to gold & silver in the market. Other crypto currencies can be used not for only store of value purpose but also a medium of exchange, to exchange native tokens with Dapps tokens, stocks, derivatives and application use.

In the internet era, people needed a circuit to connect to the internet but they don’t need to pay for accessing web sites and applications. In crypto era, people also don’t need to pay for using Dapps and playing games but need to have some tokens (including native tokens at least now). So crypto market size and price can’t be discussed only from S2F model that is applicable for commodities and natural resources especially for native tokens running applications on layer 1 blockchains. One day people wouldn’t be able to think life without web3 and decentralized applications like we can’t think life without the internet and mobile. In this essence, there must be much room for other tokens to get traction and grow more than we think with mass adoption.

From this perspective, we can try other approaches such as improving the regression model toward multinomial or multiple regression with multiple explanatory variables. Or we could use more sophisticated approaches from machine learning technique in scikit-learn library. The jupyter notebook used in this article is uploaded in github as below. [3]

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